Absract: We report on measurements of the two-dimensional intensity distribtion of linear and non-linear spin wave excitations in a LuBiFeO film. The spin wave intensity was detected with a high-resolution Brillouinlight scatteringspectroscopy setup. The observed snake-like structure of the spin wave intensity distribution is understood as a mode beating between modes with different lateral spin wave intensity distributions. The theoretical treatment of the linear regime is performed analytically, whereas the propagation of non-linear spin waves is simulated by a numerical solution of a non-linear Schrödinger equation with suitable boundary conditions.